What percent of scores would be above 592?

Question

The national average for mathematics on a standardized test in 2011 was 502. Suppose that the distribution of scores was approximately bell shaped and that the standard deviation was approximately 45.

I already found out where 68% of the scores would fall, which is 457 and 547. I just can't figure out ho to complete it.

Answer 1

Rebecca,

You're very close to your answer. You're correct, one standard deviation in each direction accounts for 68% of the scores. Two standard deviations in each direction will account for 95% of the results (range of 412 to 592) and three will account for 99.999% of the results, or effectively 100% (range of 367 to 637).

So the question is really asking for the odds of going beyond two standard deviations, but only on one side of the distribution curve. In total going from 2 standard deviations to three covers the distance between 95% and 100%, or 5%. Since we're only looking at one side of the curve, there is 2.5% chance the score will be above 592.